Graphics Reference
In-Depth Information
the most appropriate graphics for certain variables of the data set; linking will pre-
serve the multivariate context.
Although much care has been taken to ensure the best reproduction quality of
all graphics in this chapter, the reader may note that the printed reproduction in
black and white lacks clarity for some figures. Please refer to the topic's website for
an electronic version that offers full quality.
Mosaic Plots
6.2
Mosaic plots (Hartigan and Kleiner,
; Friendly,
; Hofmann,
) are prob-
ably the multivariate plots that require the most training for a data analyst. On the
other hand, mosaicplots are extremely versatile when all possible interaction and
variations are employed, as described by Hofmann (
, Chapter III.
same vol-
ume).
hissectionwillexploretypicalusesofmosaicplotsinmanydimensionsandmove
on to trellis displays.
Associations in High-dimensional Data
6.2.1
Meyer et al. (
, Chapter III.
same volume) already introduced techniques for
visualizing association structures of categorical variables using mosaicplots. Obvi-
ously, the kind of interactions we look at in high-dimensional problems is usually
more complex. Although statistical theory for categorical data oten assumes that all
variables are of equal importance, this may not be the case with real problems. Us-
ing the right order of the variables, mosaicplots can take the different roles of the
variables into account.
Example: Detergent data
For an illustration of mosaicplots and their applications, we chose to look at the
-D
problem of the detergent data set (cf. Cox and Snell,
).In this data set we look at
the following four variables:
.
Water sotness
(sot, medium, hard)
.
Temperature
(low, high)
.
M-user
(person used brand M before study)
(yes, no)
.
Preference
(brand person prefers ater test)
(X, M)
he major interest of the study is to find out whether or not preference for a deter-
gent is influenced by the brand someone uses. Looking at the interaction of M-user
and Preference will tell us that there is an interaction, but unrelated to the other two
